Minkowski formulae and Alexandrov theorems in space time

Mu Tao Wang, Ye Kai Wang, Xiangwen Zhang

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike codimension-two submanifolds in a static spherically symmetric spacetime: a codimension-two submanifold with constant normalized null expansion (null mean curvature) must lie in a shear-free (umbilical) null hypersurface. These results are generalized for higher order curvature invariants. In particular, the notion of mixed higher order mean curvature is introduced to highlight the special null geometry of the submanifold. Finally, Alexandrov type theorems are established for spacelike submanifolds with constant mixed higher order mean curvature, which are generalizations of hypersurfaces of constant Weingarten curvature in the Euclidean space.

Original languageEnglish
Pages (from-to)249-290
Number of pages42
JournalJournal of Differential Geometry
Volume105
Issue number2
DOIs
Publication statusPublished - 2017 Feb

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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